Bulletin of the American Physical Society
72nd Annual Meeting of the APS Division of Fluid Dynamics
Volume 64, Number 13
Saturday–Tuesday, November 23–26, 2019; Seattle, Washington
Session H41: Uncertainty Quantification |
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Chair: Catherine Gorle, Stanford Room: 6c |
Monday, November 25, 2019 8:00AM - 8:13AM |
H41.00001: Uncertainty quantification in CFD simulations of natural ventilation to support designing experiments for model validation Chen Chen, Catherine Gorle Natural ventilation can significantly reduce building energy consumption, but the variability in the boundary and operating conditions makes robust design a challenging task. In previous studies, a computational framework using an integral model and a computational fluid dynamics (CFD) model with uncertainty quantification (UQ) was used to predict the volume-averaged indoor air temperature during night-time ventilation in Stanford’s Y2E2 building. Comparison to point-wise building sensor measurements indicated that spatial variability in the temperature field is non-negligible. Hence, the sensor measurements might not be representative of the volume-averaged temperature. The objective of the present study is to use CFD simulations with UQ to design an experiment that optimizes temperature sensor placement to (1) obtain measurements that are representative of the volume-averaged temperature, and (2) support further analysis of the spatial variability in the temperature field for validation of CFD results. The presentation will discuss the methodology used to account for the variability in the boundary and initial conditions, the design of experiments based on the results, and the use of the measurements for validation of the model results. [Preview Abstract] |
Monday, November 25, 2019 8:13AM - 8:26AM |
H41.00002: Uncertainty quantification of the scale determination in steady RANS modeling for turbulence with large-scale structures Zengrong Hao, Catherine Gorle The scale determining variable (e.g. energy dissipation rate $\varepsilon $, frequency scale $\omega $, or length scale $l)$ is notoriously difficult to model and thus a major source of uncertainties in RANS simulations for turbulence. Particularly in the turbulence with large-scale structures that usually yield highly non-equilibrium energy spectra, a steady RANS simulation using a single modeled scale can result in considerable errors, especially for energy levels. In this report, we present a dual-scale, three-equation steady RANS approach to quantify the uncertainties originating in the scale determination in a model for the turbulence with large-scale structures (LS). The uncertainty quantification (UQ) approach is developed in three steps. First, we obtain the equations for the energies of LS and quasi-equilibrium small-scale turbulence (ST) from a triple decomposition, and employ a traditional model for the dissipation rate of ST energy. Second, under the limit condition where LS and ST have identical scales, we derive the form of the energy transfer rate (ETR) from LS to ST via a conceptual analogy with the `return-to-isotropy' evolution of Reynolds stress. Last, a marker with a single uncertain parameter is designed to identify the regions potentially bearing LS (particularly for those in large separation regions), and is used to suppress the ETR. Applications of this UQ approach in several cases show its capability of encompassing the real energy levels in the separation regions. [Preview Abstract] |
Monday, November 25, 2019 8:26AM - 8:39AM |
H41.00003: Estimating model-form uncertainty for multi-scale systems Jinlong Wu, Tapio Schneider, Andrew Stuart Global climate models (GCMs) are widely used to simulate climate change. However, their predictions have large uncertainties, arising primarily in subgrid-scale (SGS) parameterizations for globally unresolvable small-scale processes. Work to quantify parametric uncertainties in these parameterizations is underway, using methods from data analysis and machine learning. Quantifying structural or model-form uncertainties is more challenging. Here we propose a non-parametric approach to model structural errors that uses Gaussian processes and ensemble Kalman sampling and that respects physical constraints (e.g., energy conservation). We illustrate how this approach can be used to quantify model-form uncertainties in low-dimensional multi-scale systems and with an idealized GCM. The results demonstrate that this approach allows us to go beyond merely calibrating model parameters toward quantifying model uncertainty more broadly. [Preview Abstract] |
Monday, November 25, 2019 8:39AM - 8:52AM |
H41.00004: Uncertainty quantification for RANS simulations of variable density flows Aashwin Mishra, Zhu Huang, Jan Heyse, Gianluca Iaccarino, Timothy Clarke Wallstrom, David Sharp Variable density turbulent flows are widely encountered in a variety of natural phenomena and industrial applications, from the Jovian atmosphere and its Giant Red Spot to nuclear applications such as Inertial Confinement Fusion. RANS models and specifically eddy viscosity closures are widely used for investigations into variable density turbulence. However, RANS models have shortcomings in accounting for the effects of anisotropy, rotation, streamline curvature. This is further exacerbated by the forced alignment of the heat flux with the temperature gradient and the relationship between eddy diffusivity and viscosity. These assumptions lead to significant errors and uncertainties in turbulent model predictions for such flows. In this investigation, we outline the application and extension of tensor perturbations to estimate the uncertainties in variable density turbulent flows, deriving uncertainty estimates for the Besnard-Harlow-Rauenzahn (BHR) model. This is carried out for a variety of flows including tilted rocket rigs, variable density turbulent jets, etc. The selected cases show that extensionsof tensor perturbation can be utilized for uncertaintyestimationfor predictions ofvariable density turbulent flows. [Preview Abstract] |
Monday, November 25, 2019 8:52AM - 9:05AM |
H41.00005: An integrated and efficient framework for embedded Reduced Order Models for multifidelity uncertainty quantification Gianluca Geraci, Patrick Blonigan, Francesco Rizzi, Alex Gorodetsky, Kevin Carlberg, Michael Eldred Uncertainty quantification (UQ) is a key component of performing predictions using numerical simulations. Many realistic science and engineering applications require complex high-fidelity (HF) simulations for the characterization of the system's response, in combination with large numbers of random parameters that need to be propagated through these HF simulations. In these cases, a single fidelity approach for UQ becomes intractable due to the extreme cost of resolving both deterministic and stochastic errors. Multifidelity strategies have been introduced to alleviate this issue by fusing information from simulations with varying levels of fidelity, in order to obtain estimators that preserve HF statistics at much lower overall cost. This is typically accomplished through a priori definition of a sequence of model physics or discretizations of varying accuracy and expense. Less attention has been dedicated to the automatic generation of low-fidelity models using data from a small number of HF simulations. In this work, we focus on the case in which low-fidelity models are data-driven using HF samples/snapshots, with initial emphasis on projection-based reduced-order models. [Preview Abstract] |
Monday, November 25, 2019 9:05AM - 9:18AM |
H41.00006: A Multi-Fidelity Approach To Compute The Sensitivity Of A Large Eddy Simulation Walter Arias Ramirez, Nikhil Oberoi, Larsson Johan The objective of this work is to compute the sensitivity of a quantity of interest (QoI) from a large eddy simulation (LES) to variations in the problem parameters. We used the linearized RANS equations to compute the changing in the QoI based on the variation in one problem parameter. For modeling closure, we provide an inferred eddy viscosity using two different strategies. The main test case is the flow over an airfoil, with the QoI taken as the lift and/or drag. The parameter space is taken as the angle-of-attack and the Reynolds number. Here, the accuracy of the frozen eddy viscosity assumption for different parameters is assessed. [Preview Abstract] |
Monday, November 25, 2019 9:18AM - 9:31AM |
H41.00007: Implied Models Approach for Turbulence Model Form Physics-Based Uncertainty Quantification Kerry S. Klemmer, Michael E. Mueller Model form uncertainty arises from physical assumptions made in constructing models either to reduce the physical complexity or to model physical processes that are not well understood. Understanding these uncertainties is important for both quantifying prediction uncertainty and understanding the source and nature of model errors. Data-based methods for model form uncertainty quantification (UQ) are limited by the availability of data, and, in turbulence, data is often limited by Reynolds number or geometry. In contrast, physics-based UQ seeks to analyze the model form uncertainty by leveraging the physical assumptions inherent in these models so that it can be extrapolated beyond available data. In this work, an ``implied models'' approach is developed and applied to Reynolds stress modeling. In the approach, a model error transport equation is derived from the fundamental governing equations by taking the difference between the exact Reynolds stress equation and the equation implied by a particular model form. Budgets of the model error transport are analyzed to better understand the sources of error in RANS models, focusing on the relative contributions from the Boussinesq hypothesis and the specific form of the eddy viscosity in canonical turbulent flows. [Preview Abstract] |
Monday, November 25, 2019 9:31AM - 9:44AM |
H41.00008: Quantifying Uncertainties in high-fidelity Scale-Resolving Simulations of Wall Turbulence Philipp Schlatter, Saleh Rezaeiravesh, Ricardo Vinuesa We investigate how the accuracy and certainty of the quantities of interest (QoIs) of canonical wall-bounded turbulent flows are sensitive to various numerical parameters and time averaging. The scale-resolving simulations are performed by Nek5000, an open-source high-order spectral-element code. Different uncertainty quantification (UQ) techniques are utilized in the study. Using non-intrusive polynomial chaos expansion, portraits of error in the QoIs are constructed in the parameter space. The uncertain parameters are taken to be the grid spacing in different directions and the filtering parameters. As a complement to the UQ forward problems, global sensitivity analyses are performed with the results being quantified in the form of Sobol indices. Employing Bayesian optimization based on Gaussian Processes, the possibility of finding optimal combinations of parameters for obtaining QoIs with a given target accuracy is studied. To estimate the uncertainty due to time averaging, the use of different techniques such as classical, batch-based and autoregressive methods is discussed and suggestions are given on how to efficiently integrate such techniques in large-scale simulations. Comparisons of the certainty aspects between high-order and low-order codes (OpenFOAM) are given. [Preview Abstract] |
Monday, November 25, 2019 9:44AM - 9:57AM |
H41.00009: Surrogate Modeling for Fluid Flows Using Physics-Constrained, Label-Free Deep Learning Jian-Xun Wang, Luning Sun, Han Gao, Shaowu Pan Numerical simulations on fluid dynamics problems can often be computational prohibitive for most real-time and many-query applications, and developing a cost-effective surrogate model is of great practical significance. Deep learning (DL) has shown new promises for surrogate modeling due to its capability of handling strong nonlinearity and high dimensionality. However, the off-the-shelf DL architectures fail to operate when the data becomes sparse, which is often the case in most parametric fluid dynamics problems since each data point in the parameter space requires an expensive numerical simulation. In this paper, we provide a physics-constrained DL approach for surrogate fluid modeling without relying on any simulation data. Specifically, a structured deep neural network (DNN) architecture is devised to enforce the boundary conditions, and the Navier-Stokes equations are used to drive the training. Numerical experiments are conducted on a number of vascular flows and forward propagation of uncertainties in fluid properties and domain geometry is studied as well. The results show excellent agreement on the flow field and propagated uncertainties between the DL surrogate approximations and the first-principle numerical simulations. [Preview Abstract] |
Monday, November 25, 2019 9:57AM - 10:10AM |
H41.00010: Stochastic Simulation of Flow Instabilities in a Rotating Cylinder S. Hadi Seyedi, Ali Akhavan-Safaei, John Foss, Mohsen Zayernouri A rotating cylinder subject to an imperfect/ random rotational brake system is modeled and simulated to better understand the stochastic nonlinear nature of vorticity dynamics, arising from the uncertain initial/ boundary/ topological conditions. The rotating cylinder, fully filled with water, arrives at rest within a short time-period from a constant rotational speed. We employ spectral element method to perform highly-accurate, complex-geometry capturing, and cost-efficient direct numerical simulation of the fluid flow. Given available experimental (PIV) data, the corresponding forward and backward uncertainty quantifications are also performed. This study leads to the Bayesian inference of the stochastic brake system input parameters in addition to the investigation of forward uncertainty propagation from the available data and model into the flow fields, hence predictive simulations of flow instabilities. [Preview Abstract] |
Monday, November 25, 2019 10:10AM - 10:23AM |
H41.00011: Least-Squares Petrov--Galerkin Reduced-Order Models for Hypersonic Flight Vehicles Patrick Blonigan, Francesco Rizzi, Micah Howard, Jeff Fike, Kevin Carlberg High-speed aerospace engineering applications rely heavily on computational fluid dynamics (CFD) models for design and analysis due to the expense and difficulty of flight tests and experiments. This reliance on CFD models necessitates performing accurate and reliable uncertainty quantification (UQ). However, it is very computationally expensive to run CFD for hypersonic flows due to high grid resolution requirements. Additionally, UQ methods are “many-query” problems requiring many runs with a wide range of input parameters. One way to enable computationally expensive models to be used in such many-query problems is to employ projection-based reduced-order models (ROMs) in lieu of the (high-fidelity) full-order model. In particular, the least-squares Petrov–Galerkin (LSPG) ROM (equipped with hyper-reduction) has demonstrated the ability to significantly reduce simulation costs while retaining high levels of accuracy on a range of problems including subsonic CFD applications. This work presents the first application of LSPG to hypersonic CFD problems including the Blottner sphere and HiFIRE experimental flight vehicle. This shows the ability of LSPG ROMs to significantly reduce computational costs while maintaining high levels of accuracy in computed quantities of interest. [Preview Abstract] |
Monday, November 25, 2019 10:23AM - 10:36AM |
H41.00012: Dynamically bi-orthonormal formulation for stochastic partial differential equations Prerna Patil, Hessam Babaee A new method is presented for a real-time reduced-order modeling of transient stochastic systems for the purpose of uncertainty propagation. We present a closed-form evolution equation for a low-rank time-dependent basis that evolves with the dynamics. An on-the-fly reduction of the dynamical system is then obtained by projecting the full-dimensional system onto to the low-rank basis. The presented method is compared against the state of the art Dynamically Orthogonal (DO) method and Bi-Orthogonal (BO) method for highly ill-conditioned cases. In particular, we demonstrate that the presented method preserves the accuracy of the solution and the shape of the modes as the system passes through a low eigenvalue phase. The results for several demonstration cases are presented, including linear advection equation, stochastic Burgers' equation and stochastic flow in a channel. [Preview Abstract] |
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